Chaos, metastability and ergodicity in Bose-Hubbard superfluid circuits

Arwas, Geva; Cohen, Doron

doi:10.1063/1.5016126

Cited by 3 publications

(3 citation statements)

References 45 publications

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“…In a dynamical protocol, therefore, the current would not be conserved [44]. Nevertheless, I(Ω) will be denoted as 'persistent current' in analogy of the current states of the continuous theory (see also [45]). Important insights on the current states of the system can be obtained by the current's fluctuations…”

Section: Model System and Observablesmentioning

confidence: 99%

Exact results for persistent currents of two bosons in a ring lattice

et al. 2020

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We study the ground state of two interacting bosonic particles confined in a ring-shaped lattice potential and subjected to a synthetic magnetic flux. The system is described by the Bose-Hubbard model and solved exactly through a plane-wave Ansatz of the wave function. We obtain energies and correlation functions of the system both for repulsive and attractive interactions. In contrast with the one-dimensional continuous theory described by the Lieb-Liniger model, in the lattice case we prove that the center of mass of the two particles is coupled with its relative coordinate. Distinctive features clearly emerge in the persistent current of the system. While for repulsive bosons the persistent current displays a periodicity given by the standard flux quantum for any interaction strength, in the attractive case the flux quantum becomes fractionalized in a manner that depends on the interaction. We also study the density after the long time expansion of the system which provides an experimentally accessible route to detect persistent currents in cold atom settings. Our results can be used to benchmark approximate schemes for the many-body problem.

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Section: Model System and Observablesmentioning

confidence: 99%

Exact results for persistent currents of two bosons in a ring lattice

et al. 2020

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“…8 . Further studies on condensate rings (with number of sites N s ≥ 3) investigated different theoretical aspects including dynamical and thermodynamical stability 11,12 , chaos and ergodicity 13,14 , symmetry analysis and ef-fects of quantum many-body dynamics 15 and quantum quenches 16 . However, in those works, the values of the circular currents were not investigated in detail in the chaotic regime, and time scales associated with the currents were not discussed.…”

Section: Introductionmentioning

confidence: 99%

Chaos onset in large rings of Bose-Einstein condensates

Wozniak¹,

Kroha²,

Posazhennikova³

2022

Preprint

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We consider large rings of weakly-coupled Bose-Einstein condensates, analyzing their transition to chaotic dynamics and loss of coherence. Initially, a ring is considered to be in an eigenstate, i.e. in a commensurate configuration with equal site fillings and equal phase differences between neighboring sites. Such a ring should exhibit a circulating current whose value will depend on the initial, non-zero phase difference. The appearance of such currents is a signature of an established coherence along the ring. If phase difference falls between π/2 and 3π/2 and interparticle interaction in condensates exceeds a critical interaction value uc, the coherence is supposed to be quickly destroyed because the system enters a chaotic regime due to inherent instabilities. This is, however, only a part of the story. It turns out that chaotic dynamics and resulting averaging of circular current to zero is generally offset by a critical time-scale tc, which is almost two orders of magnitude larger than the one expected from the linear stability analysis. We study the critical time-scale in detail in a broad parameter range.

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“…In few mode bosonic systems, micro-canonical thermalization has been investigated using a semi-classical analysis [17][18][19][20][21][22][23]. In these works, the loss of initial state memory is explained by the appearance of chaos in the corresponding classical system as opposed to a direct analysis of eigenstates.…”

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confidence: 99%

Thermalization and its Breakdown for a Large Nonlinear Spin

Kelly,

Timmermans,

Tsai

2019

Preprint

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By developing a semi-classical analysis based on the Eigenstate Thermalization Hypothesis, we determine the long time behavior of a large spin evolving with a nonlinear Hamiltonian. Despite integrable classical dynamics, we find the Eigenstate Thermalization Hypothesis is satisfied in the majority of eigenstates and thermalization is generic. The exception is a novel mechanism for the breakdown of thermalization based on an unstable fixed point in the classical dynamics. Using the semi-classical analysis we derive how the equilibrium values of observables encode properties of the initial state. We conclude with a discussion of relevant experiments and the potential generality of this mechanism for the breakdown of thermalization.

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Chaos, metastability and ergodicity in Bose-Hubbard superfluid circuits

Cited by 3 publications

References 45 publications

Exact results for persistent currents of two bosons in a ring lattice

Exact results for persistent currents of two bosons in a ring lattice

Chaos onset in large rings of Bose-Einstein condensates

Thermalization and its Breakdown for a Large Nonlinear Spin

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